1. Field of the Invention
The invention relates to devices and methods for detecting, quantifying, indicating or otherwise responding to the polarization characteristics of an input electromagnetic signal, specifically a light input signal. The invention also relates to measurement of polarization aspects of light such as degree of polarization, extinction ratio measurements and one or two dimensional polarization mapping.
Multiple measurements are taken in conjunction with filters and/or waveplates that process light or selectively pass portions of the input signal. These measurements discriminate among light signals having distinct polarization states or polarization components, by taking measurements at different relative phase relations and/or different orientations in space or time. According to an inventive aspect, the measurements are taken using certain tunable elements, arranged to provide the necessary diversity of measurement states to resolve polarization information and optionally wavelength information. Moreover, in addition to enabling the measurements, this technique facilitates calibration that can be automated and employed without external reference signals, and allows controlled optimization of the measurement states used, to obtain the greatest accuracy of which the device is capable.
According to an inventive aspect, a novel calibration technique is provided. The calibration comprises comparison of input signals having one or more polarization attributes that are known to be related in a way that can be checked mathematically. A device transfer function containing a matrix of factors is adjusted so that the measurement sets obtained in this way, achieve values that prove true according to the known values or relationships.
In a preferred arrangement, the calibration, optimization and measurement aspects of the invention are under control of a processor that operates tunable elements in the input signal path(s) to selectively control optimization and calibration conditions. Preferably, controllable birefringence elements, optionally including narrow band wavelength bandpass filters, are tuned for selective optimization, or optimization within certain conditions or for selected wavelengths.
The input for the calibration process can be one or more arbitrary quasi-monochromatic input signals with diverse polarization components. The polarization characteristics of the signals are measured through a matrix of scaling or similar factors representing the device matrix, i.e., the factors defining the transfer function of the measurement signal path. Along one or more signal paths, at least one polarization transformation occurs. However, the at least one attribute that can be checked mathematically, as described above, remains true before and after the transformation. Thus the transformed and un-transformed signals provide distinct measurement sets that when checked should still prove true. Calibration of the device comprises adjusting the matrix of factors representing the device matrix, if necessary, so that the at least one attribute as measured is made to be true.
A plurality of different measurements are taken on signals or transformed versions of signals, of which any two or more signals or versions share at least one attribute that can be checked as true. Preferably, twelve or more polarization transformations are applied to one given input signal. Measurements are taken for each one. An iterative process is then accomplished as described herein, for homing in on a correctly calibrated matrix of coefficients or factors of the characteristic instrument matrix that accurately define the response characteristics of the polarization measurement system, i.e., the calibrated response to any arbitrary input. This technique permits calibration without the need for any calibrated reference input (although the input needs to have diverse polarization components to fully exercise the measurement signal paths).
Attributes which can be checked, and which can be the attribute(s) checked for true to test and correct calibration, might be any of various attributes and/or relationships between attributes that should remain true in a calibrated unit. Exemplary polarization transformations might comprise differential phase delay through a waveplate or reorientation or the like. Examples of attributes that are not changed by a particular transformation could include the degree of linear polarization (independent of the axis of orientation), the Stokes S3 variable value, or other attributes as discussed herein. Whether a given attribute or relationship remains true after a polarization transformation depends on the nature of the transformation, in a known manner.
Concepts employed with respect to calibration are further employed according to the invention to optimize the measurements that are taken. This is advantageous according to the invention because different transformations as discussed above regarding calibration steps, can be made tunably and/or automatically selectable, and thus can be chosen to arrive at optimal sets of measurements capable of obtaining the greatest distinctions between measurement values obtained for light inputs of different polarization states. Such selections are used to choose the most spatially- or temporally-separated instrument states that are available and that exercise the largest available scale of measurement of the device. A theoretical explanation of the physical implications of factors in a Muller Matrix, in conjunction with the Jones reciprocal matrix, is provided herein as an aid to understanding.
2. Prior Art
The polarization state of an electromagnetic wave such as a light wave can be quantified uniquely by reference to four Stokes parameters. The four values of the Stokes parameters make up a Stokes vector.
The Stokes vector can have four values, S0, S1, S2, S3, which encode intensity as well as the distribution of the intensity among components of different relative orientation and phase. It is frequently helpful to ignore absolute intensity and to consider only polarization. For that purpose, three Stokes values, S1, S2, S3, are considered. Assuming that the intensity is a constant, the three Stokes values (which now encode the relative intensity as a function of orientation and phase) can be graphed to points on the surface of a sphere because they meet the mathematical definition of a sphere, S12+S22+S32=R2. For a nominal unit sphere, R=1. The values of S1, S2 and S3 can vary between xe2x88x921.0 and +1.0. Based on the sum of the squares begin equal to one, however, if any of the Stokes values is equal to one, then the others must be zero (indicating a particular exclusive polarization state). The S1 variable encodes between vertical and horizontal polarization orientations. The S2 variable is associated with xc2x145xc2x0. The S3 variable is associated with clockwise versus counterclockwise circular orientation (i.e., orthogonal component phase difference between xc2x190xc2x0).
For encoding Stokes values, the orientation of reference system used is relevant to whether the intensity falls into one of the S values or another. However, the values of a Stokes vector in one frame of reference are readily transformable to comparable values for the same light wave according to a different frame of reference.
In a polarization analysis unit, it is convenient to consider a frame of reference in which the Z axis is the propagation axis, an X-Y plane is perpendicular or normal to the Z axis, and optical elements such as polarizing filters and/or waveplates have some orientation relative to the X-Y-Z coordinate system. In a polarization analysis unit with plural optical elements (each having some orientation and position in the X-Y-Z coordinate system) and perhaps also plural optical paths, the relative position and alignment of the various elements affect the measurements that are obtained.
The polarization state of light can vary with wavelength. A given beam of light may have a certain proportion at a particular wavelength polarized one way and another portion perhaps at a different wavelength or another time segment polarized another way. Such variations need to be taken into account in order to compare results of polarization measurements. It may be difficult or impossible to determine the polarization state of a wideband signal, although it may be possible to sample by taking a number of polarization analysis unit readings at different substantially-monochrome wavelengths or different time segments.
Small differences in relative position and orientation of components can complicate the problem of measuring polarization parameters. For example, changes in temperature of the measurement unit can affect the results of polarization measurements.
A polarization measurement unit or polarization analysis unit can contain devices such as a succession of filters and detectors, intended to respond exclusively to light in a given polarization state. A polarization analysis unit, such as a polarimeter, may have sufficient number (at least four) functional units intended separately to detect particular polarization attributes.
The responses of plural devices can vary and also can overlap. The relationship for determining the output values (e.g., Stokes values) that correspond to raw input measurements, can be defined by a matrix of weighting factors representing the extent to which incremental raw measurement values respectively affect one or more output values. Assuming that a measurement unit is provided with sufficient detection devices to obtain at least some raw measurement response to light energy contributing to Stokes variables independently, then such a matrix relationship can be used to calculate the correct output from a set of raw data values. It should be noted, however, that some useful polarization analyses may not involve Stokes parameter values or may only require partial information on the Stokes parameters.
One challenge is to determine accurately what the matrix factors should be. This is to calibrate the polarization analysis unit. The relationship of the output of the measurement unit to an input light signal needs to be determined, and encoded as a mathematical transfer function. The transfer function relating plural inputs to plural outputs is a device matrix and ideally defines accurately the output Stokes values that correspond to all possible raw data measurements, by providing the relationship by which any combination of input values are convertible to the corresponding correct output values. Calibrating by accurately choosing a matrix of inter-related factors can be a complicated problem.
In many fields of measurement, calibration of a device comprises applying a known reference input, observing the output of the device and adjusting the device to cause the observed output to correspond to the output that the known reference input should produce if the device is accurately calibrated. However, this is not always practical because of the requirement for the accurate standard of reference, in this case accurate information defining the polarization state of the input reference signal. Furthermore, on the very small scale of a wavelength, calibration is appropriate frequently because temperature variations and other minor variations can have a large effect on the output data. It would be advantageous if an accurate, quick and preferably automated technique would make calibration more readily available, at least as a means of refining some predetermined values that may be obtained based on a theoretical modeling of components, such as birefringent components, static or tunable wave plates and other elements of a polarization analysis unit
An exemplary polarization analysis unit, such as a polarimeter, could contain an optical measurement head for collecting raw data values for distinct polarization states, a processing unit to operate on the collected data using a device matrix as the transformation factors, and a calibration unit to control and effect changes to the device matrix. The polarimeter can have any arbitrary angular orientation in an X-Y plane relative to a propagation axis of an incident light beam. In order to detect the polarization state of the incident beam, the measurement head makes several raw measurements (at least four) from the input light. These measurements include variations in angular orientation, retardation, and other polarization sensitive attributes, sufficient so that the measurements vary, at least somewhat, with all possible variations in polarization characteristics of the input signal. Preferably, each possible polarization state corresponds to a unique set of input values.
It may be necessary to recalibrate a polarization analysis unit frequently in order to correct for errors that arise from unavoidable short term changes such as temperature changes, vibration, etc., as well as long term changes such as are caused by component aging. Assuming that the raw input measurements encompass the full range of polarization-related parameters, recalibration may be achieved by adjusting the factors used in the transfer function employed by the processing unit when converting raw measurement data into polarization data.
As mentioned above, a conventional technique for calibrating any measurement device comprises using the device to measure a reference standard having known characteristics as to the parameter to be measured. The resulting measurement value is observed. The device is adjusted, if necessary, to cause the output of the device to equal the measurement values that the reference standard should produce.
One measurement achieves accuracy at a given measurement value, but the object is correct measurement at all values. One calibration measurement may be sufficient if the calibration is simply adjustment of a variable offset value such as the tare weight on an otherwise calibrated scale. At least two calibration measurements at different values are needed if the calibration involves adjustment of gain or proportion. Three measurements may be needed to adjust offset and gain. A larger number of measurements may be needed if there is a nonlinear relationship between the input and the output. These considerations apply to measuring one value. In the case of polarization, there are four values that need to be measured (three if normalized for intensity) to define uniquely the polarization state of light.
To make multiple test measurements in calibrating measurement devices, generally speaking, two or more known calibration reference standards are advantageous. U.S. Pat. No. 5,296,913xe2x80x94Heffner discloses an example of a calibration scheme for a polarimeter, involving plural polarization state measurements.
Heffner corrects raw measurement values of which there are typically four. The object in Heffner is to correct the gain or proportioning of the sensing circuits used to collect intensity data measurements. However, there is a larger and much more complicated problem involved in calibrating a polarimeter or a polarization analysis unit, namely the extent to which raw measurements taken for each of the four or more raw measurement channels contribute to the Stokes measurement values that are needed at the output. This relationship changes with environment and also needs to be calibrated to obtain accurate measurement results.
Optical polarization state measurement techniques have different types that are related, because the same discrimination functions (at least four) must be handled by any of the types in order to take all the necessary measurements. The different types transform and discriminate for components of the input signal in spatially or temporally different ways. One type or technique uses pairs of two optical elements, such as a linear polarizer and a quarter waveplate. Combinations of such optical elements provide for measurements at different orientations and at different phases. It is possible to achieve a given polarization state discrimination function with alternative configurations of spatial position, angular orientation, phase retardation, reflection, etc. The configuration of the elements must provide a group that includes a sufficiently diverse set so that the group responds distinctively to light at each of the four polarization characteristics.
A second type or technique can have a timing aspect. The polarization state of the light input is modulated, for example by rotating elements, or at a higher frequency, by one or several phase modulators. The resulting periodic changes in the detected intensity at the modulation or rotation frequency can be resolved out, effectively providing plural measurements of transforms of the input light signal, which provide Stokes parameter values.
One type or technique comprises beam splitting to produce a set of beams that individually lead into distinct discrimination and measurement devices along parallel beam paths downstream from a beam splitter. The intensity of the input is subdivided among the downstream paths in this so-called xe2x80x9cdivision of amplitudexe2x80x9d (DOA) scheme. Such a parallel path scheme enables the four Stokes parameters to be measured simultaneously or repetitively at a high rate, thereby preventing confusion if the input light signal has time-varying polarization characteristics. Separation of the paths and the possibility of differences from nominal position and orientation may introduce other demands, but these can be accommodated, particularly by accurate and frequent calibration.
In a division of amplitude (DOA) technique, the incident electromagnetic wave is split into several beams. The beam splitting component can be polarization sensitive or not. If polarization sensitive, then the beam splitting component can provide one of the means for discriminating among polarization states. Alternatively, the input wave can be split into beams so as to divide the incident energy in a polarization independent way, but in that case the respective split beams are applied to detectors that discriminate for polarization components of input light at distinct polarization states.
A polarization-independent splitting has potential advantages. The initial split does not introduce potential polarization-dependent errors. The split beam portions can have balanced intensity, regardless of the input applied, which helps to ensure that a reasonably robust intensity is available at each of the parallel measurement stages.
A four-detector arrangement that might be applicable to a photo-polarimeter, wherein light is successively reflected from one detector to the next, through a succession of four photo-detectors, is disclosed in R. M. A. Azzam, xe2x80x9cArrangement of Four Photodetectors for Measuring the State of Polarization of Light.,xe2x80x9d Opt. Lett. 10, 309-311 (1985). The photo-detectors are theoretically oriented so that each detects a distinct polarization parameter. Each successive reflection in Azzam alters the polarization orientation of the incident input, due to the reflection. The reflected beams, which thus are processed or split serially into successive segments having distinct polarization orientations, each impinge on an associated detector that is correctly placed and oriented. The photodetectors in the device advantageously have special coatings, to balance the beam intensity at each of the successive detectors and to improve efficiency. The geometry needed, particularly to obtain high accuracy measurements using a specific set of reflection angles, does not lead readily to a compact size. Because of the complex relation and limited tunability between the incident angle and the polarization response, the structure is difficult to optimize to achieve the optimum performance.
A similar setup that utilizes a special prism and two Wollaston prisms to generate beams of four different polarization states is disclosed in Compain and Drevillon, xe2x80x9cBroadband Division of Amplitude Polarimeter Based on Uncoated Prisms,xe2x80x9d Applied Optics 37, 5938-5944 (1998). The geometry of this device, including the special prism, likewise does not lead to a compact size. In addition, the accuracy of this device is not optimized and appears difficult to optimize.
Techniques using reflection gratings to split beams in a polarization dependent way have been discussed. A polarization dependent split is provided by a reflection-type metal-coated grating disclosed in R. M. A Azzam, Appl. Opt. 31, 3574 (1992). The polarization dependence of this type of splitting is not highly discriminating, which affects the resulting measurement accuracy. Polarizers included at various angles to each of the beams can improve accuracy, but are not wholly optimal because of the non-optimized configuration.
A largely polarization independent beamsplitting is suggested using a transmission grating laboratory setup in Cui and Azzam, xe2x80x9cSixteen-Beam Grating-Based Division-of-Amplitude Photopolarimeter,xe2x80x9d Opt. Lett. 21, 89-91 (1996). The sixteen separate split beams are applied to polarizers at various angles, and a quarter wave plate is interposed in the path of one of the beams. The large number of beams in such a device permits a varied set of measurement operations, but is arguably redundant and inefficient. A low intensity source may become too weak for accurate measurement when divided by sixteen. The device also is somewhat impractical because a low dispersion grating is needed to generate sixteen beams, and a rather long diverging distance is needed for the beam separation to provide enough space to admit polarizers and intensity responsive photodetectors for each separate beam, rendering the overall device rather large. The polarized plus one waveplate, although commonly used in many polarization measurement setups, is not an optimized configuration.
The challenges in the design and configuration of a polarization analysis unit include high speed, high accuracy, high efficiency and compact size. It is a substantial challenge to achieve all these attributes at once. Division of amplitude polarimeters have the potential for short duration and high speed repetitive measurements, due to their simultaneous rather than consecutive nature, but the overall operational speed is not entirely a matter of the type of optical measurement head used. There are other complexities of concern, such as processing requirements and calibration needs, among others.
The polarization analysis unit of the present invention has certain alignment angles and phase retardations of the waveplates, which affect the polarization analysis unit""s noise immunity. In the context of serial measurements rather than in a division of amplitude arrangement, the prior art addresses orientation and phase angle issues in Ambirajan and Look, xe2x80x9cOptimum Angles for a Polarimeter: Part I,xe2x80x9d Opt. Eng. 34, 1651-1655 (1995). The reference uses four quarter-waveplates. A retardance of 132xc2x0 and retarder orientation angles of xc2x151.7xc2x0 and xc2x115.1xc2x0 are considered optimal for a serial measurement scheme in Sabatke, et al. xe2x80x9cOptimization of Retardance for a Complete Stokes Polarimeter,xe2x80x9d Opt. Lett. 25, 802-804 (2000).
Polarization analysis units such as a polarimeter require four measurements to provide four distinct measurements of parameters that complete define the polarization state of a given input signal. The general idea of a four measurement polarimeter is uncomplicated. The Stokes vector factors that define a multi-faceted polarization state can be represented by a vector S that has the necessary number of elements to define a polarization state. If a particular electromagnetic signal has a polarization state with Stokes values in a signal vector represented by I, and is measured using a polarimeter instrument that in turn has a transfer function A, then I=AS or S=Axe2x88x921I, where A is the so-called the instrument matrix that specifies the response of the instrument to a nominal input. Instrument matrix A can be an Nxc3x974 matrix for any N that is greater than or equal to 4.
For convenience in this description, but not to imply any loss of generality, the number of applicable matrix elements is limited to N=4. We can assume that the instrument matrix A is not singular (i.e., the polarimeter is not precalibrated and ideal). To minimize the system""s sensitivity to the fluctuation of I, the determinant of A should be as large as possible. To meet these criteria, several configurations have been proposed in the prior art.
One proposal is a division of amplitude polarization analysis unit based on quarter-wave plates at four orientations, followed by a polarizer at 0 degree. The largest possible value of the determinant is 1.487, which is achieved at orientations xc2x115.1xc2x0, xc2x151.7xc2x0, or xc2x138.3xc2x0, xc2x174.9xc2x0. By comparison, a configuration is xe2x88x9245xc2x0, 0xc2x0, 30xc2x0, 60xc2x0 is calculated to a determinant of 1.4.
In another proposal, quarter-wave plates at four orientations/directions, are followed by four polarizers at different directions. The largest possible value of the determinant is 3.079. However, because this arrangement has eight parameters to be optimized. A single optimized solution may be possible, but it is not believed to be known.
A further possibility is a division of amplitude polarization analysis unit with waveplates at four directions, followed by a polarizer at 0xc2x0. Phase retardation by the waveplates provides additional variables for optimization. The largest possible value of the determinant is 3.079 (at orientations xc2x115.1xc2x0, xc2x151.7xc2x0, and waveplate retardation of 132xc2x0).
It is an object of the invention to provide a high speed, high accuracy polarization analysis unit, optionally with measurements as a function of wavelength.
The invention includes aspects for optimizing the polarization analysis unit by certain at least four-measurement techniques.
A technique for calibration of the measurement device includes converting a light source having at least one known aspect and/or relationship between aspects related to polarization, to a new orientation or distribution, followed by re-measurement and a conversion to derive mathematically a value corresponding to the known aspect and/or relationship between aspects, whereupon the apparatus can be calibrated by conforming the derived value to the value of the known aspect and/or relationship between aspects.
A novel method and device are provided for measuring the polarization state of an electromagnetic wave. The device is compact, lightweight, accurate, high speed, and flexible, allowing a variety of input formats for the light and providing a variety of output formats for the polarization data. Spectral data can also be obtained through the use of a novel wavelength tunable polarizer in the disclosed device. The invention relates in part to a particular arrangement for an optical measurement head as well as the polarization transformation. The invention also comprises processing steps applied to the data, and includes variations in forms of output of measured and derived parameters.
The device provides efficient and well-balanced, polarization-independent amplitude splitting. One example is to use a diffractive beamsplitter generating a small number of beams (typically, five beams) at high dispersion, which permits the device to be made compact. Four waveplates are interposed (one in each of four of the beams), preferably at optimal orientations and with optimal phase retardance values, to enhance the accuracy of the polarization measurement. These aspects are optimized to minimize the effect of raw measurement error on the ultimate determination of polarization state. Another approach includes the use of polarization insensitive beam splitter. This polarization insensitive beam splitter can be designed and made, for example, using dielectric coating. By cascading several beamsplitters in series and/or in parallel, the well-balanced beam separation can be achieved.
A novel wavelength tunable polarizer preferably is included, providing a technique to derive spectral information along with polarization states of the input light.
The inventive polarization analysis unit can determine the polarization state of the incident light in a high speed snap measurement and/or repetitively at a high rate. A unique hybrid analog/digital processing unit preferably preserves the speed advantages of the division of amplitude method for recording the raw measurements. The processing unit also assists in maintaining the accuracy of the raw measurements.
The novel spectral capabilities of the device derive from, for example, the use of a tunable birefringent Fabry-Perot interferometer in the analyzer stage of the polarization analysis unit. When a tunable linear, birefringent medium is inserted into a Fabry-Perot interferometer the transmission of the interferometer can be polarization and wavelength dependent. A tunable birefringent material such as a liquid crystal has two distinct axes (the so-called ordinary and extraordinary axes) with different indices of refraction. The phase retardation along one axis is typically controlled electrically, providing a means to electrically adjust the wavelength at which the interferometer is resonant. Light at a specific wavelength (or an integer multiple) that is linearly polarized parallel to the resonant axis (ordinary or extraordinary) is transmitted, typically with a high degree of discrimination.
The indices of refraction and the structure of the interferometer can be chosen so that only one axis (preferably the electrically tunable extraordinary axis) has this transmission resonance aspect in the wavelength band of interest. In this way, the Fabry-Perot interferometer or etalon functions as a wavelength tunable linear polarizer.
The novel spectral capabilities of the device can also be derived from the use of Cholesteric liquid crystal. the cholesteric liquid crystal (CLC) is also a nematic type, except that the structure acquires a spontaneous twist about an axis normal to the preferred molecules"" directions. Because of this twisted director profile, the CLC materials are not homogeneous, and they show many interesting optical properties, especially with respect to the propagation and reflection of light. They selectively reflect light of a definite polarization and definite wavelength.
In a preferred arrangement, the polarization analysis unit is operated using control software that can report in various formats, can report to remote locations, and admits of automated or remotely initiated calibration.
In another preferred embodiment, calibration is achieved using successive transformations of sets of Stokes polarization parameters derived from five input measurements, with characteristic parameters making it possible to calibrate by comparing successive measurements achieved from an arbitrary input signal that is sufficiently diverse to have produce values across sets of Stokes parameters. For this purpose, the elements of the input are shuffled to produce a new set of Stokes parameters that have an aspect in common with a previous set produced from the same input signal, which provides a calibration technique based on an arbitrary signal input.
The polarization analysis unit of the invention can measure beams propagating in fibers or in free space. As such, it is capable of measuring the degree of polarization of spatially incoherent beams. Polarization analysis units based upon single mode fiber designs are, in principle, unable to make such a measurement.